与M-矩阵相关的一类二次矩阵方程的新迭代法  

New Iteration Method for a Quadratic Matrix Equation Associated with an M-Matrix

作　　者：关晋瑞[1] 宋儒瑛[1] Zubair Ahmed GUAN Jinrui;SONG Ruying;ZUBAIR Ahmed(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China;Institute of Mathematics and Computer Science,University of Sindh,Sindh 76080,Pakistan)

机构地区：[1]太原师范学院数学系,山西晋中030619 [2]信德大学数学与计算机系,巴基斯坦信德76080

出　　处：《应用数学》2021年第1期1-7,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (11401424);the Natural Science Foundation of Shanxi Province (201901D211423);the Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi (2019L0783)。

摘　　要：本文研究与M-矩阵相关的一类二次矩阵方程的数值解法.这类方程源于马尔可夫链的带噪Wiener-Hopf问题,其解中具有实际意义的是M-矩阵解.通过简单的变换,将该二次矩阵方程转化为M-矩阵代数Riccati方程.提出一种新的迭代方法,并对其进行收敛性分析.数值实验表明,新的迭代方法是可行的,且在一定条件下比现有的一些方法更为有效.In this paper,we consider numerical solution of a quadratic matrix equation associated with an M-matrix,which arises in the study of noisy Wiener-Hopf problems for the Markov chain.The solution of practical interest is the M-matrix solution.By a simple transformation,this quadratic matrix equation is transformed into an M-matrix algebraic Riccati equation.We propose a new iteration method for this equation and then give the convergence analysis of it.Numerical experiments are given to show that the new iteration method is feasible and effective than some existing methods in some cases.

关 键 词：二次矩阵方程 M-矩阵 代数RICCATI方程 迭代法 

分 类 号：O241.6[理学—计算数学]